<html><body bgcolor="#FFFFFF"><div>Another good one is the mutilated checkerboard problem: can you tile a checkerboard with 1x2 dominoes if two diagonally opposed squares have been removed?</div><div><br></div><div>It's a great introduction to the concept of proof:  visually and kinesthetically accessible, with a very simple but non-obvious solution.  Usually my students get sufficiently engaged with it that they really want to know for sure if it's impossible.</div><div><br></div><div>Hofstadter's MIU-puzzle is similar in spirit but much more language-oriented. <br><br>Best,<div>Jordan</div><div><br></div></div><div><br>On Nov 19, 2009, at 5:10 PM, Stephen Bloch <<a href="mailto:sbloch@adelphi.edu">sbloch@adelphi.edu</a>> wrote:<br><br></div><div></div><blockquote type="cite"><div><br><div class="AppleOriginalContents"><div>On Nov 19, 2009, at 4:59 PM, Neil Toronto wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>Jon Rafkind wrote:<br><blockquote type="cite"><a href="http://www.maa.org/devlin/LockhartsLament.pdf">http://www.maa.org/devlin/LockhartsLament.pdf</a><br></blockquote><font class="Apple-style-span" color="#006312"><br></font>Does anybody know of a list of example problems like the ones he gives in the essay? I'd love to have a big list of math teasers to draw from for dinner conversation with my kids.<br></div></blockquote></div><br><div>Well, you could take a look at "CS Unplugged".</div><div><br></div><div>Of course there are Fibonacci numbers.  How much bigger is each Fibonacci number than the previous one?  The ratio seems to be alternating bigger and smaller, but the "bigger" and "smaller" are getting closer to one another.  Where will they meet?  Is this number interesting in any other ways?  What if I started the Fibonacci sequence with something other than 1 and 1?</div><div><br></div><div>Use your calculator (or, better yet, DrScheme) to write various fractions in decimal.  Some of them end after a fixed number of digits, while others repeat digits indefinitely.  Which are which?  1/9 repeats a single digit forever; 1/11 repeats a pair of digits forever; 1/7 repeats six digits forever.  Can you predict, given the number n, whether 1/n will be repeating, and if so, how many digits will be in the repeating pattern?  What if you write it in a base other than ten?</div><div><br></div></div></blockquote><blockquote type="cite"><div><span>_________________________________________________</span><br><span>  For list-related administrative tasks:</span><br><span>  <a href="http://list.cs.brown.edu/mailman/listinfo/plt-scheme"><a href="http://list.cs.brown.edu/mailman/listinfo/plt-scheme">http://list.cs.brown.edu/mailman/listinfo/plt-scheme</a></a></span><br></div></blockquote></body></html>